cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A344259 For any number n with binary expansion (b(1), ..., b(k)), the binary expansion of a(n) is (b(1), ..., b(ceiling(k/2))).

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%I A344259 #15 May 15 2021 01:43:52
%S A344259 0,1,1,1,2,2,3,3,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,4,4,
%T A344259 4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,8,
%U A344259 8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10
%N A344259 For any number n with binary expansion (b(1), ..., b(k)), the binary expansion of a(n) is (b(1), ..., b(ceiling(k/2))).
%C A344259 Leading zeros are ignored.
%H A344259 Rémy Sigrist, <a href="/A344259/b344259.txt">Table of n, a(n) for n = 0..8191</a>
%H A344259 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A344259 a(A020330(n)) = n.
%F A344259 a(A006995(n+1)) = A162751(n).
%F A344259 a(n XOR A344220(n)) = a(n) (where XOR denotes the bitwise XOR operator).
%e A344259 The first terms, alongside their binary expansion, are:
%e A344259   n   a(n)  bin(n)  bin(a(n))
%e A344259   --  ----  ------  ---------
%e A344259    0     0       0          0
%e A344259    1     1       1          1
%e A344259    2     1      10          1
%e A344259    3     1      11          1
%e A344259    4     2     100         10
%e A344259    5     2     101         10
%e A344259    6     3     110         11
%e A344259    7     3     111         11
%e A344259    8     2    1000         10
%e A344259    9     2    1001         10
%e A344259   10     2    1010         10
%e A344259   11     2    1011         10
%e A344259   12     3    1100         11
%e A344259   13     3    1101         11
%e A344259   14     3    1110         11
%e A344259   15     3    1111         11
%t A344259 Array[FromDigits[First@Partition[l=IntegerDigits[#,2],Ceiling[Length@l/2]],2]&,100,0] (* _Giorgos Kalogeropoulos_, May 14 2021 *)
%o A344259 (PARI) a(n) = n\2^(#binary(n)\2)
%o A344259 (Python)
%o A344259 def a(n): b = bin(n)[2:]; return int(b[:(len(b)+1)//2], 2)
%o A344259 print([a(n) for n in range(85)]) # _Michael S. Branicky_, May 14 2021
%Y A344259 Cf. A006995, A020330, A162751, A344220.
%K A344259 nonn,base,easy
%O A344259 0,5
%A A344259 _Rémy Sigrist_, May 13 2021